Effects of spin-orbit coupling in superconducting proximity devices: Application to ${\mathrm{CoSi}}_2/{\mathrm{TiSi}}_2$ heterostructures

Motivated by the recent findings of unconventional superconductivity in $\mathrm{Co}{\mathrm{Si}}_2/\mathrm{Ti}{\mathrm{Si}}_2$ heterostructures, we study the effect of interface-induced Rashba spin-orbit coupling on the conductance of a three-terminal T-shaped superconducting device. We calculate the differential conductance for this device within the quasiclassical formalism that includes the mixing of triplet-singlet pairing due to the Rashba spin-orbit coupling. We discuss our result in light of the conductance spectra reported by S.-P. Chiu et al., arXiv:2012.13679 for $\mathrm{Co}{\mathrm{Si}}_2/\mathrm{Ti}{\mathrm{Si}}_2$ heterostructures.

Figure 1

Schematic illustration of a T-shaped junction. The three-terminal proximity device consists of a diffusive normal metal (NM) part attached to a superconductor (SC). The blue area indicates the diffusive normal metal (NM) part of the device, while the orange area shows the SC part.

Figure 2

Differential conductance for a T-shaped junction attached to a superconductor under the influence of Rashba SOC. The parameter $r$ is the ratio of the triplet component to singlet component of the order parameter. The interface quality parameter $\mathrm{\Gamma }$ is set to 20. The ratio of lengths along the two spatial directions $L_y/L_x$ is 0.1, 0.5, and 1 in (a), (b), and (c), respectively. The differential conductance is calculated in the zero-temperature limit.

Figure 3

The differential conductance for a T-shaped junction of a $dp$ superconductor for several values of $r$ with a larger singlet component. The length along the $\widehat{y}$ direction is $0.5L_y$.

Figure 4

The differential conductance for a T-shaped junction of a $df$ superconductor for several values of $r$. The length along the $\widehat{y}$ direction is $0.5L_y$. The orientation of the $d_{x^2-y^2}$ orbital form factor is shown in the main plot. The leg of the T junction is taken along the $\widehat{y}$ direction, and the voltage is applied along the $\widehat{x}$ direction.

Figure 5

The differential conductance for a T-shaped junction of a $dp$ superconductor for several values of $r$. The length along the $\widehat{y}$ direction is $0.5L_y$. The orientation of the $d_{xy}$ orbital form factor is shown in the main plot. The leg of the T junction is taken along the $\widehat{y}$ direction, and the voltage is applied along the $\widehat{x}$ direction.